Radiation hydrodynamics with neutrinos - Variable Eddington factor method for core-collapse supernova simulations

Neutrino transport and neutrino interactions in dense matter play a crucial role in stellar core collapse, supernova explosions and neutron star formation. Here we present a detailed description of a new numerical code for treating the time and energy dependent neutrino transport in hydrodynamical simulations of such events. The code is based on a variable Eddington factor method to deal with the integro-differential character of the Boltzmann equation. The moments of the neutrino distribution function and the energy and lepton number exchange with the stellar medium are determined by iteratively solving the zeroth and first order moment equations in combination with a model Boltzmann equation. The latter is discretized on a grid of tangent rays. The integration of the transport equations and the neutrino source terms is performed in a time-implicit way. In the present version of the program, the transport part is coupled to an explicit hydrodynamics code which follows the evolution of the stellar plasma by a finite-volume method with piecewise parabolic interpolation, using a Riemann solver to calculate the hydrodynamic states. The neutrino source terms are implemented in an operator-split step. Neutrino transport and hydrodynamics can be calculated with different spatial grids and different time steps. The structure of the described code is modular and offers a high degree of flexibility for an application to relativistic and multi-dimensional problems at different levels of refinement and accuracy. We critically evaluate results for a number of test cases, including neutrino transport in rapidly moving stellar media and approximate relativistic core collapse, and suggest a path for generalizing the code to be used in multi-dimensional simulations of convection in neutron stars and supernovae.